Thanks, Jim. I do indeed have this inclination. In fact my original
intent was to use the simple pendulum to learn and apply the Runge-
Kutta Method. I just haven't gotten around to it yet. Might your
suggestion be a variation of this?
Cheers, Roger
Roger,
Actually I was thinking of something even simpler than the
Runge-Kutta approximation.
Using the Euler approximation, the repeat loop to generate the
pendulum motion is really simple and looks like this:
repeat until the mouseClick
setRA r,270+psi -- Polar coordinates; 270 so that the pendulum hands DOWN
add -c*psi to angVel --Add angular acceleration to the angular velocity
add angVel to psi --Add angular velocity to the angle
end repeat
where psi is the angular displacement of the pendulum.
I am using Turtle Graphics, but I think you get the idea. To see this
in action, put this in the message box:
go stack url "http://home.infostations.net/jhurley/ControlGraphics.rev";
and go to the last card.
Control graphics is a variation on TG. It allows you to identify any
control as a Turtle which not only responds to Transcript, but also
to TG. So you can create a circle graphic and call it "pendulum" and
then talk to the circle like it was a turtle, i.e. forward 10, right
90, setXY 20,30, setRA 200,35 etc.
Polar coordinates are particularly useful in the pendulum problem
I tried to show the dependence of the period on the amplitude but no
luck so far. Maybe Runga-Kutta is required.
The period depends on the amplitude (to second order in the
amplitude) in this way:
T = T(0) (1 + A^2/16)
where A is the angular amplitude in radians.
Jim
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